"I welcome the substantial assistance in Japan's legislation to
repair its troubled banking system," declared President Clinton this
weekend. But what exactly have the Japanese done? Some press reports suggest
that the most important part of the package - the injection of capital
into the biggest banks - will face trouble, because the banks themselves
do not want the money. I have been trying to understand all this, and offer
the following illustrative example.

Imagine a bank with 105 billion yen in deposits, whose assets consist
of loans with a face value of 115 billion yen. (Yes, Japanese banks have
stocks and land as well, but this will not change the principle). Unfortunately,
many of these loans are of doubtful quality. Let's suppose that there is
a 50 percent chance that Japan's economy will improve, and all the loans
will be repaid; but there is also a 50 percent chance that the bank will
get only 85 billion yen.

In terms of expected value, this bank is insolvent - it has a net worth
of minus 5 billion. But its stock will have a positive value, which is
essentially due to the deposit insurance "put". Ignoring risk
premia, the value of the stock will be 0.5(115-105) = 5 billion yen.

Now along comes the government, offering to inject capital into the
bank, by buying preferred stock - in effect, by giving the bank a loan
that is senior to the equity but subordinate to the deposits. Say the government
offers 5 billion. In the plan as currently described, this money would
come with strings attached: the bank would have to write off bad debts,
etc.. But we can also imagine a "soft money" version of the plan,
in which the money is given without questions asked. In the best case,
it turns out, the bank is indifferent. More likely, the bank will positively
disdain the offer.

First consider the conditional capital injection. We may represent this
in a stylized way by supposing that the bank is forced to revalue its assets
at their true expected value. This immediately wipes out the stockholders
(not to mention the managers). I don't think the bank will ask for money
under those conditions.

Alternatively, suppose no questions are asked. The bank's assets are
now 115 loans plus 5 billion government bonds, with a supposed capital
of 10 billion, half of which is a government claim in the form of preferred
stock. If things go well, then, the original owners will receive 10 billion
(120 - 110). If they go badly, as before, the owners get nothing. So their
expected payoff is unchanged.

Notice, incidentally, that if the government bought common stock
rather than preferred, the return to the original shareholders would actually
be reduced (to 3.75). The basic logic here is the essential theorem of
financial moral hazard: if you can borrow money without regard for risk
- which is what deposit insurance does - you want to maximize leverage
and hence minimize capital.

So there doesn't seem to be any reason why Japan's big banks, which
surely are either underwater or close to it if their assets were marked
to market, would accept the government's offer without coercion.

Finally, suppose that the government were in fact to simply give this
bank money, say by buying off some of its questionable loans at par. Would
this make the bank more willing to lend? On the contrary: If the logic
of moral hazard applies - and the unwillingness of the banks to accept
capital injections suggests that it does - better capitalized banks will
be less willing to make risky loans, because they will care more
about the left tail of the distribution of returns.

Strange, isn't it? The Japanese bank bailout is supposedly the key to
the recovery of Japan's economy, which is supposedly the key to recovery
in Asia; optimism sparked by that bailout has fueled a definite improvement
in the mood in the whole region. Yet a simple example suggests that the
rescue program is likely to end in farce, as banks decline to be rescued;
and that if somehow the Japanese government finds the will to force the
banks to take money anyway, it will actually be counterproductive.